A diffusion equation is used to predict the sound propagation in long rooms with diffusely reflecting boundaries. The model is defined by two parameters, the coefficient of diffusion depending on the mean free path, and an exchange coefficient expressing wall absorption. The diffusion equation is solved for time-varying sources and in stationary state. Analytical expressions of the sound attenuation and reverberation in infinite, semi-infinite and finite long rooms are quite in accordance with numerical simulations of diffuse sound field. It is also shown that the diffusion model allows to predict experimental observations: the decay curves are not linear, the reverberation time increases with the source-receiver distance, and sound attenuation is linear along corridors. The dependence of the coefficient of diffusion with the degree of wall diffusion is also discussed.